




from ....utils import logging


UpperCamelCase__ :   Dict						=							logging.get_logger(__name__)







class 				lowerCAmelCase_       (					lowerCamelCase_							):






				def __init__(			self      ,snake_case__      ,snake_case__=None      ,snake_case__=2048 ):
							SCREAMING_SNAKE_CASE_   : int					  =      config.__dict__
							SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      modal_hidden_size
							if num_labels:
										SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      num_labels




"""simple docstring"""


a				=range(2, 20 + 1)
a				=[10**k for k in range(ks[-1] + 1)]
a				={}





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Any:




						'''simple docstring'''



						lowerCamelCase__   =sum(a_i[j] for j in range(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							)							)
						lowerCamelCase__   =sum(a_i[j] * base[j] for j in range(min(len(__lowerCAmelCase							)  ,       __lowerCAmelCase							)							)							)

						lowerCamelCase__   , lowerCamelCase__   =0, 0
						lowerCamelCase__   =n - i

						lowerCamelCase__   =memo.get(__lowerCAmelCase							)

						if sub_memo is not None:
												lowerCamelCase__   =sub_memo.get(__lowerCAmelCase							)

												if jumps is not None and len(__lowerCAmelCase							) > 0:
																		# find and make the largest jump without going over
																		lowerCamelCase__   =-1
																		for _k in range(len(__lowerCAmelCase							) - 1  ,       -1  ,       -1							):
																								if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																														lowerCamelCase__   =_k
																														break

																		if max_jump >= 0:
																								lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =jumps[max_jump]
																								# since the difference between jumps is cached, add c
																								lowerCamelCase__   =diff + c
																								for j in range(min(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							)							):
																														lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
																								if new_c > 0:
																														add(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)

												else:
																		lowerCamelCase__   =[]
						else:
												lowerCamelCase__   ={c: []}
												lowerCamelCase__   =sub_memo

						if dn >= max_dn or c + diff >= base[k]:
												return diff, dn

						if k > ks[0]:
												while True:
																		# keep doing smaller jumps
																		lowerCamelCase__   , lowerCamelCase__   =next_term(__lowerCAmelCase  ,       k - 1  ,       i + dn  ,       __lowerCAmelCase							)
																		diff += _diff
																		dn += terms_jumped

																		if dn >= max_dn or c + diff >= base[k]:
																								break
						else:
												# would be too small a jump, just compute sequential terms instead
												lowerCamelCase__   , lowerCamelCase__   =compute(__lowerCAmelCase  ,       __lowerCAmelCase  ,       i + dn  ,       __lowerCAmelCase							)
												diff += _diff
												dn += terms_jumped

						lowerCamelCase__   =sub_memo[c]

						# keep jumps sorted by # of terms skipped
						lowerCamelCase__   =0
						while j < len(__lowerCAmelCase							):
												if jumps[j][1] > dn:
																		break
												j += 1

						# cache the jump for this value digitsum(b) and c
						sub_memo[c].insert(__lowerCAmelCase  ,       (diff, dn, k)							)
						return (diff, dn)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   List[str]:




						'''simple docstring'''



						if i >= n:
												return 0, i
						if k > len(__lowerCAmelCase							):
												a_i.extend([0 for _ in range(k - len(__lowerCAmelCase							)							)]							)

						# note: a_i -> b * 10^k + c
						# ds_b -> digitsum(b)
						# ds_c -> digitsum(c)
						lowerCamelCase__   =i
						lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =0, 0, 0
						for j in range(len(__lowerCAmelCase							)							):
												if j >= k:
																		ds_b += a_i[j]
												else:
																		ds_c += a_i[j]

						while i < n:
												i += 1
												lowerCamelCase__   =ds_c + ds_b
												diff += addend
												lowerCamelCase__   =0
												for j in range(__lowerCAmelCase							):
																		lowerCamelCase__   =a_i[j] + addend
																		lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)

																		ds_c += a_i[j]

												if addend > 0:
																		break

						if addend > 0:
												add(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						return diff, i - start_i





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						for j in range(__lowerCAmelCase  ,       len(__lowerCAmelCase							)							):
												lowerCamelCase__   =digits[j] + addend
												if s >= 10:
																		lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
																		lowerCamelCase__   =addend // 10 + quotient
												else:
																		lowerCamelCase__   =s
																		lowerCamelCase__   =addend // 10

												if addend == 0:
																		break

						while addend > 0:
												lowerCamelCase__   , lowerCamelCase__   =divmod(__lowerCAmelCase  ,       10							)
												digits.append(__lowerCAmelCase							)





def      lowerCamelCase_					(   __lowerCAmelCase = 10**15							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[1]
						lowerCamelCase__   =1
						lowerCamelCase__   =0
						while True:
												lowerCamelCase__   , lowerCamelCase__   =next_term(__lowerCAmelCase  ,       20  ,       i + dn  ,       __lowerCAmelCase							)
												dn += terms_jumped
												if dn == n - i:
																		break

						lowerCamelCase__   =0
						for j in range(len(__lowerCAmelCase							)							):
												a_n += digits[j] * 10**j
						return a_n


if __name__ == "__main__":
	print(F'''{solution() = }''')


